Is it a good practice to choose my undergraduate research topic on my own? Can I get enough help?

(This question is one of three correlated questions: How should I do it? (second part), What are the downsides? (third part).This is the first part)

I am an undergraduate student (in Computer Engineering) and I will be starting undergraduate research for my thesis. I have talked with many professors about possible projects and all the projects they proposed to me seemed interesting enough.

During summer, though, I read a paper and I was very interested and excited about it, but this paper was not for the projects that were proposed to me, but in a different area. I would like to do research in this area but I have some questions, because none of my professor is doing research in this particular field.

So, my questions are:

1. 
   

   Should I try to do a project in that area, even though my professors aren’t doing research in that particular topic (some do research in a close field) or choose one of the projects that were proposed to me?

   
   


2. 
   
   

   Will any professor be able to help/guide me through the project, even if he is not doing research in this topic exactly? (I will ask them if they are capable of helping me, but I want to know, how much can someone help me if he is in the same field but I am doing something different than his projects)

   
   

P.S. I want to understand whether it will be beneficial to do a project that I want to do because of some paper(s) that I read or it will be better to do a project that was proposed to me. Also, I would like to go for a Ph.D. after I graduate.